This paper proves that a multiplicity of certainty equilibria is not necessary for the existence of
sunspot effects in two-period general equilibrium models with incomplete markets. Sunspot effects are present, by definition, when real economic variables differ across realizations of extrinsic uncertainty.
For the class of models delineated above and further restricted to numeraire assets whose payouts are identical across such realizations, the literature has remained silent on whether a multiplicity of certainty equilibria is necessary for sunspot effects. First, I prove that such a multiplicity is not necessary for sunspot effects in this particular class of models. Second, I prove that, over an entire set of economies commonly considered in sunspot examples, an equilibrium with sunspot effects can never be characterized as a randomization over multiple certainty equilibria.